Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature
Fengbo Hang, Xiaodong Wang
TL;DR
This paper establishes boundary rigidity results for hemispheres with positive Ricci curvature, advancing the understanding of geometric structures under curvature constraints and addressing a Ricci curvature analogue of Min-Oo's conjecture.
Contribution
It proves new boundary rigidity theorems for compact manifolds with boundary under Ricci curvature bounds, extending previous scalar curvature results.
Findings
Boundary rigidity for hemispheres with Ricci curvature bounds
Confirmation of a Ricci curvature version of Min-Oo's conjecture
Advancement in geometric analysis of manifolds with boundary
Abstract
We prove some boundary rigidity results for the hemisphere under a lower bound for Ricci curvature. The main result can be viewed as the Ricci version of a conjecture of Min-Oo.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations